TITLE: Is here a specific name for the following theorem? (Sides of inscribed squares of a triangle meet at points collinear with a vertex of the triangle)
QUESTION [22 upvotes]: For any acute and right triangle, two of the intersections(C and B) of the two inscribed squares and the vertex A of the triangle are collinear.
I have a proof for the theorem, but I have not found any specific name for it. I searched "inscribed squares in a triangle," and I still could not find the same shape. Can anyone provide a specific name for this, or a way that I can find the theorem online?
For the similar question concerning the cubes inscribed in a tetrahedron, please visit Extend squares inscribed in a triangle to the cubes inscribed in a tetrahedron
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Proof: 
$\tan(\angle ACB) = \frac{IK}{KC}$ 
$\because LG = IK$
$\therefore \frac{LG}{KC} = \frac{IK}{KC} = \tan(\angle ACB)$
Similarly,
$\frac{LH}{JC} = \tan(\angle ACB)$
$\because \angle LHO = \angle LGO = \angle OLC = \angle OKC = 90^{\circ}$
$\therefore \angle JCK = \angle GLH = 360^{\circ} - \angle LHO - \angle LGO - \angle GOH = 360^{\circ} - \angle OJC - \angle OKC - \angle JOK $
$\because \frac{LH}{JC} = \frac{LG}{KC} = \tan(\angle ACB), \angle JCK = \angle GLH$
$\therefore \Delta LHG \simeq \Delta CJK $ (SAS)
$\therefore \angle LGH = \angle JKC$
$\because \angle LGO = \angle OKC = 90^{\circ}$
$\therefore \angle HGO = \angle OKJ = \angle LGO - \angle LGH = \angle OKC -\angle JKC$
Similarly, $\angle GHO = \angle OJK$
$\therefore \Delta GOH \simeq \Delta KOJ$ (AA)
$\therefore \frac{GH}{JK} = \frac{LG}{KC}$
$\therefore \frac{GO}{OK} = \frac{LG}{KC} = \frac{GH}{JK}$
$\because \angle LGO = \angle OKC$
$\therefore \Delta LGO \simeq \Delta CKO$ (SAS)
$\therefore \angle GOL = \angle KOC$
Similarly, $\angle HOL = \angle JOC$
$\because \angle IOJ = \angle POK$
$\therefore \angle LOG + \angle IOJ + \angle JOC = \angle COK + \angle POK + \angle HOL = \frac{1}{2}(360^{\circ}) = 180^{\circ}$
$\therefore$ Points C, O, L are collinear
$Q.E.D$

REPLY [2 votes]: Although interesting, this theorem is not new. I recently found the article "Squares Inscribed in Angles and Triangles" on JSTOR.

Bailey, Herbert, and Duane Detemple. “Squares Inscribed in Angles and Triangles.” Mathematics Magazine, vol. 71, no. 4, 1998, pp. 278–284. JSTOR, JSTOR, www.jstor.org/stable/2690699.
It would be nice if I am the person who discovered the fact, but since the theorem was published in 1998, the credit does not belong to me.